I'm having great difficulty in getting started with this question let alone solving it, Any help would be much appreciated.

A boat that has a speed in still water or 1.8ms^-1 crosses a river that flows due north at a speed of 0.54ms^ -1. It starts from a point on the east bank and is pointed in the direction S33W. Take i to be 1ms^-1 due east and j to be 1ms^-1 due north. Also, take

Vb to be the velocity of the boat in still water,

Vr to be the velocity of the river,

V to be the resultant velocity of the boat.

(a) Express each of the vectors Vb and Vr in component form, giving the components to 4dp.

(b) Hence show that the resultant velocity V of the boat is given in component form, approximately by V = -0.9804i - 0.9696j

(c) By putting V into geometric form, find the overall speed |V| of the boat, (in ms^-1 to 2dp), and its direction of travel as a bearing (with the angel correct to 1dp).

(d) Suppose that the river has a constant width of 24 metres. how long (in secs) does it take the boat to cross the river, and how far (in metres) upstream or downstream has it travelled from its starting point? give answers to 1dp.

ThanksJon

Jan 14th 2009, 05:34 AM

earboth

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Originally Posted by nojcarter

Hi,

I'm having great difficulty in getting started with this question let alone solving it, Any help would be much appreciated.

A boat that has a speed in still water or 1.8ms^-1 crosses a river that flows due north at a speed of 0.54ms^ -1. It starts from a point on the east bank and is pointed in the direction S33W. Take i to be 1ms^-1 due east and j to be 1ms^-1 due north. Also, take

Vb to be the velocity of the boat in still water,

Vr to be the velocity of the river,

V to be the resultant velocity of the boat.

(a) Express each of the vectors Vb and Vr in component form, giving the components to 4dp.

(b) Hence show that the resultant velocity V of the boat is given in component form, approximately by V = -0.9804i - 0.9696j

(c) By putting V into geometric form, find the overall speed |V| of the boat, (in ms^-1 to 2dp), and its direction of travel as a bearing (with the angel correct to 1dp).

(d) Suppose that the river has a constant width of 24 metres. how long (in secs) does it take the boat to cross the river, and how far (in metres) upstream or downstream has it travelled from its starting point? give answers to 1dp.

ThanksJon

1. The positive x-axis points East.

2. The angle of S33°W equals an angle of 237° measured counterclockwise from the positive x-axis.

3. Using this angle the vectors $\displaystyle \overrightarrow{v_b}$ and $\displaystyle \overrightarrow{v_r}$ can be written as: